PC-12 Captain reported a NMAC at an airport after the tower was closed. The slower aircraft was not communicating their intentions until final approach. The crew executed a 360 degree turn with the concurrence of ATC, then landed.

We were arriving into ZZZ, RNAV Z Runway XX. Conditions were VMC. The First Officer (FO) was Pilot Flying (PF). I was Pilot Monitoring (PM). Approximately 15 miles from the airport outside ZZZZZ (IF) I noticed ADS-B traffic paralleling the final approach course. The tower was closed and I was monitoring CTAF while communicating with ZZZ Approach. We were cleared for the approach after which ATC issued their first traffic alert. We continued the approach while scanning for traffic. We were unable to establish visual contact with the other aircraft but continued to monitor their position on TCAS. The other aircraft did not make any announcement on CTAF. ATC issued additional traffic alerts (2 or 3 more times) each time with closing proximity. Once established on final, ATC asked us if we could accept a VISUAL approach so that we could maneuver to avoid the traffic. We accepted the VISUAL. It became clear that we were on the same course with the other airplane and as we began to gain and close on them, we decided to maintain our current altitude to avoid descending into them. ATC had kept us with them longer than usual and I decided to ask for a frequency change so I could attempt to communicate with the other aircraft. As I changed frequency we realized we were directly over the other aircraft approximately 400 feet above. We were also close to the airport and unable to make a normal descent for a landing. I returned to ATC requested a left 360. As we circled, I broadcasted on CTAF directly to the other aircraft at which time he made his first transmission stating that he was about to land. He landed and failed to report clear of the runway until queried by me. This type of VFR NORAD operation is increasingly common under the class Bravo shelf. It is not in violation of any regulation but is not safe. The presence of a class D airspace at least mandates two-way radio communication. After landing we informed the passengers that the circling maneuver was executed to allow another aircraft to land before us. They were all aware of this unusual maneuver and appreciated the explanation. There was never an immediate danger during this incident but there certainly could have been. It is clear to me that the potential for a disaster exists. These occurrences at ZZZ have become more frequent and are happening more than occasionally. It is not an exaggeration to say that the frequency of these occurrences combined with the potential outcome being catastrophic make continued operation into ZZZ a significant safety risk, especially with the tower closed and no regulation requiring two-way communication.